Answer:
400g
Step-by-step explanation:
mass= density × volume
Substitute the given value of density and volume.
Mass of the object
= 4(100)
= 400g
Fifteen hundred students attend Biship Ryan High School. 120 students were asked "Do you think that Library hours should be extended?" 40 students agreed that hours should be extended, 10 said they were against extended hours, and 70 students had no opinion. The school newspaper reported: "80% of students who had an opinion agree that school library hours should be extended". Is this a valid inference? Justify your reasoning.
Answer:
The inference is valid.
Step-by-step explanation:
In this case we need to test whether, 80% of students who had an opinion agree that school library hours should be extended.
A sample of 120 students were selected.
Of these 120, 50 students had an opinion and 70 did not.
Since we need to test for the students having an opinion, the sample size is, n = 50.
The sample proportion of students who had an opinion and agreed is:
[tex]\hat p=\frac{40}{50}=0.80[/tex]
The hypothesis can be defined as follows:
H₀: The proportion of students who had an opinion agree that school library hours should be extended is 80%, i.e. p = 0.80.
Hₐ: The proportion of students who had an opinion agree that school library hours should be extended is different from 80%, i.e. p ≠ 0.80.
The z-test for single proportion will be used.
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.80-0.80}{\sqrt{\frac{0.80(1-0.80}{50}}}=0[/tex]
The test statistic value is 0.
Compute the p-value of the test:
[tex]p-value=2\times P (Z < 0)\\=2\times 0.50\\=1[/tex]
The p-value of the test is 1.
The p-value is very large, so the null hypothesis will not be rejected at any significance level.
Thus, it can be concluded that the proportion of students who had an opinion agree that school library hours should be extended is 80%.
Hence, the inference is valid.
Ashton and Kamir are arguing about how a number trick they heard goes. Ashton tells Andrew to think of a number, multiply it by five and subtract three from the result. Kamir tells Andrew to think of a number, add five and multiply the result by three. Andrew says that whichever way he does the trick he gets the same answer. What was the number?key
Answer: The number was 9.
Step-by-step explanation:
Let the number be 'x;.
think of a number, multiply it by five and subtract three from the result :
According to Ashton, the expression would be :
[tex]5x-3[/tex]
Kamir tells Andrew to think of a number, add five and multiply the result by three:
According to Kamir, the expression would be :
[tex]3(x+5)[/tex]
At last, they get the same number :
[tex]5x-3=3(x+5)\\\\5x-3=3x+15\\\\5x-3x=15+3\\\\2x=18\\\\x=\dfrac{18}{2}\\\\x=9[/tex]
Hence, the number was 9.
By comparing Ashton's algebraic expression '5x-3' with Kamir's expression '3(x+5)', one can find that if these expressions are equal, the number x that Andrew was thinking of is 15.
Explanation:The subject of this question is Mathematics and it is suitable for a Middle School grade level. The trick that Ashton and Kamir are trying to figure out is based on one of the basic properties of numbers. Andrew says that regardless of the trick, he gets the same answer. This implies that the operations used in both tricks must have equivalent results. Let's use algebraic expressions to represent the steps in each trick. If the original number Andrew thinks of is x:
According to Andrew, these expressions are equal. So, we have the equation:
5x - 3 = 3(x + 5)
By solving this equation, you can find the original number that Andrew was thinking about, which is 15.
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if you roll a six-sided die, what is the probability of rolling a number greater than 2?
Answer:1/6
Step-by-step explanation:
When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population grew at a rate of P'(t) = 45(1+sqrt(t)).
a) what is the population after 15 years?
b) find the popuation P(t) at any time t > 0.
Answer:
(a) The population after 15 years is 2678.
(b)Therefore the population P(t) at any time t>0 is
[tex]P(t)= 45t+30 {t^{\frac32}}+260[/tex]
Step-by-step explanation:
Given that,
The population grew at a rate of
[tex]P'(t)=45(1+\sqrt t)[/tex]
Integrating both sides
[tex]\int P'(t) dt=\int 45(1+\sqrt t)dt[/tex]
[tex]\Rightarrow \int P'(t) dt=\int (45+45\sqrt t)dt[/tex]
[tex]\Rightarrow \int P'(t) dt=\int 45\ dt+\int 45\sqrt t\ dt[/tex]
[tex]\Rightarrow P(t)= 45t+45\ \frac{t^{\frac12+1}}{\frac12+1}+c[/tex] [ c is integration constant]
[tex]\Rightarrow P(t)= 45t+45\ \frac{t^{\frac32}}{\frac32}+c[/tex]
[tex]\Rightarrow P(t)= 45t+45\times\frac 23 \times {t^{\frac32}}+c[/tex]
[tex]\Rightarrow P(t)= 45t+30 {t^{\frac32}}+c[/tex]
When t=0 , P(0)= 260
[tex]\therefore 260= 45\times0+30\times {0^{\frac32}}+c[/tex]
[tex]\Rightarrow c=260[/tex]
[tex]\therefore P(t)= 45t+30 {t^{\frac32}}+260[/tex]
Therefore the population P(t) at any time t>0 is
[tex]P(t)= 45t+30 {t^{\frac32}}+260[/tex]
To find the population after 15 years, we need to plug t=15 in the above expression.
[tex]P(15)=( 45\times 15)+30( {15^{\frac32}})+260[/tex]
≈2678
The population after 15 years is 2678.
P = 9r +3q
Work out the value of P when r = 6 and q = -4
P =
Answer:
p= 9(6)+3(-4)
p= 42
hope this help
Answer:
42
Step-by-step explanation:
P=9r+3q
When q equals to a negative 4 and when r is aswell the number 6.It means to substitute
P=9(6)+3(-4)
p=54-12
p=42
At Robin's Snow Cones, the shaved ice portion of the cone is shaped like a perfect sphere with a diameter of 8 cm. Exactly half of the shaved ice sphere extends above the paper cup holder. What is the volume of ice that extends above the cup to the nearest cubic centimeter? In your calculations, use LaTeX: \pi\:=\:3.14
Answer:
The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3
Step-by-step explanation:
Solution:-
- The shaved ice is modeled as a sphere.
- The half of the shaved ice sphere extends above the cup holder.
- The volume of sphere with radius r = diameter d / 2 :
[tex]V = \frac{4}{3}*\pi *r^3[/tex]
- We are to calculate the volume of the extended part of the sphere with diameter d = 8 cm or radius r = 4 cm.
- The volume of hemisphere is:
[tex]V = \frac{1}{2} *\frac{4}{3}*3.14 *r^3= \frac{2}{3}*3.14 *r^3\\\\V = \frac{2}{3}*3.14 *4^3 \\\\V =134.04128 cm^3[/tex]
- The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3
Solve for n:
3⁄5 · n = 6
Answer:
n = 10
Step-by-step explanation:
Solve for n:
(3 n)/5 = 6
Multiply both sides of (3 n)/5 = 6 by 5/3:
(5×3 n)/(3×5) = 5/3×6
5/3×3/5 = (5×3)/(3×5):
(5×3)/(3×5) n = 5/3×6
5/3×6 = (5×6)/3:
(5×3 n)/(3×5) = (5×6)/3
(5×3 n)/(3×5) = (3×5)/(3×5)×n = n:
n = (5×6)/3
6/3 = (3×2)/3 = 2:
n = 5×2
5×2 = 10:
Answer: n = 10
To solve for n in 3⁄5 · n = 6, divide both sides of the equation by 3⁄5. The solution is n = 10.
Explanation:To solve for n in the equation 3⁄5 · n = 6, we need to isolate n on one side of the equation. To do this, we can divide both sides of the equation by 3⁄5, which is the same as multiplying both sides by its reciprocal, 5⁄3. This cancels out the fraction on the left side, leaving us with n = 6 × 5⁄3. Multiplying 6 by 5 gives us 30, and dividing that by 3 gives us a final answer of n = 10.
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In ΔKLM, the measure of ∠M=90°, the measure of ∠L=48°, and KL = 28 feet. Find the length of LM to the nearest tenth of a foot
Answer: x= 18.7357 or 18.7 feet
What is the slope of the line that passes through the points (-9, 10)(−9,10) and (21, 15) ?(21,15)?
Answer:
1/6 or 1.666667
Step-by-step explanation:
(y2-y1)/(x2-x1)
(15-10)/(21- -9) = 1/6
Answer:
1/6
Step-by-step explanation:
Consider the matrix show below:
(See picture)
Which matrix below represents Nt?
Answer:
The Answer is B
Step-by-step explanation:
Put the equation into desmos.com/matrix
it is a 2 row, 2 column matrix, hit Enter
Next line, press the letter A, then press the A^t button and it will give you the answer.
The transpose of matrix N is represented by b. [7 0 3 -2 ] , which correctly reflects the switching of rows and columns in the original matrix.
The correct answer is option B.
To find the transpose ([tex]N^t[/tex]) of a matrix N, we need to switch its rows and columns. Let's calculate the transpose of the given matrix N:
Matrix N:
```
N = [ 7 3 ]
[ 0 -2 ]
```
Transpose of N ([tex]N^t[/tex]):
```
[tex]N^t[/tex]= [ 7 0 ]
[ 3 -2 ]
```
So, the transpose of matrix N is:
```
[tex]N^t[/tex] = [ 7 0 ]
[ 3 -2 ]
```
Now, let's compare the transpose we calculated with the options provided:
a. [ 0 -2 7 3 ] - This is not the transpose of N.
b. [7 0 3 -2 ] - This is the transpose of N.
c. [3 7 -2 0 ] - This is not the transpose of N.
d. [-2 3 0 7] - This is not the transpose of N.
So, the correct answer is option b:
```
[tex]N^t[/tex] = [7 0 3 -2 ]
```
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To start a board game,the player who rolls two sixes gets to go first. What is the probability that a player will roll two
number cubes and get two sixes?
) Intro
Done
There is a 1/36 or a ~2.8% chance that a player will roll two sixes. Because the dice is cubed, the player will have a 1/6 probability of rolling a six one time. Because the player needs to get six 2 times in a row, you would simply need to multiply 1/6 by itself twice(1/6•1/6 or 1/6^2) which equals 1/36.
Holly has $462 in her bank account and takes out $15 each week but does not put any back in. Write an equation/expression to represent the amount of money she has in her bank account.
Answer:
Therefore required expression is
y =462 - t×15
where y represents the amount of money in her bank account in dollar after t week.
Step-by-step explanation:
Given that,
Holly has $462 in her bank account and takes out $15 each week but does not put any back in.
She takes out $15 on first week.
The remaining amount of her bank account is =$(462-15)
=$(462 - 1×15)
If she withdraws $15 on second week.
The remaining amount of her bank account is =$(462-15-15)
=$(462 - 2×15)
Similarly after third the amount in her account is =$(462 - 3×15)
From the above it is cleared that
The amount in her account after t week is
=$(462 - t×15)
Therefore required expression is
y =462 - t×15
where y represents the amount of money in her bank account in dollar after t week.
In the United States, 36 percent of the people have a blood type that is A positive. From a random sample of 150 people from Norway, 66 had a blood type that was A positive. Consider a hypothesis test to investigate whether the proportion of people in Norway with a blood type of A positive is different from that in the United States. Which of the following is the standard deviation used to calculate the test statistic for the one-sample z-test? (0.24) (0.76) 150 (0.44) (0.56) 150 (0.36)(0.64) 150 (0.44)(0.56) 150 (0.36 (0.64) 150
Answer:
The standard deviation used to calculate the test statistic for the one-sample z-test is 0.04.
Step-by-step explanation:
A single proportion z-test can be performed to determine whether the proportion of people in Norway with a blood type of A positive is different from that in the United States.
It is provided that the percentage of people in the US with blood type A positive is, p = 36%.
A random sample of n = 150 people from Norway are selected to check the above claim.
The hypothesis can be defined as:
H₀: The proportion of people in Norway with a blood type of A positive is same as that in the United States, i.e. p = 0.36.
Hₐ: The proportion of people in Norway with a blood type of A positive is different from that in the United States, i.e. p ≠ 0.36.
The test statistic for the the hypothesis testing is:
[tex]z=\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
The mean of the sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
Compute the standard deviation value as follows:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]=\sqrt{\frac{0.36(1-0.36)}{150}}[/tex]
[tex]=0.03919184\\\approx0.04[/tex]
Thus, the standard deviation used to calculate the test statistic for the one-sample z-test is 0.04.
What is the measure of Au?
889
44°
50°
64°
92°
Answer:
50
Step-by-step explanation:
The measure of AU is 50.
What is an arc?An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
Given:
arc QU = 88 and <QUA = 111
QDA = 2 <QUA
= 2 X 111
= 222
Now, QUA = 360- 222 = 138
arc AU = QUA - arc QU
= 138- 58
= 50
Hence, the measure of AU is 50.
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if a triangle has a base of 16 meters and a height of 10 meters, what is the area?
Answer:
A = 80 m^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base length and h is the height
A = 1/2 (16) *10
A = 80 m^2
Answer:
A = 80
Step-by-step explanation:
A = .5bh
A = .5(16)(10)
A = 80
Can I get brainliest
A research team conducted a critical study, and constructed a 95% confidence interval from their data. The team was not happy with the result because they felt the margin of error was much too large. All other things being equal, if they were to repeat the study, what could they do to reduce the margin of error?
A) They could construct the confidence interval with a lower confidence level than they previouslyused.B) They could include a greater number of subjects in the experiment.C) They could reduce the population standard deviation ?.D) All of the above are possible things for them to try.E) None of the above will work because of the randomness in the experiment.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample mean ± margin of error
Margin of error = z × population standard deviation/sample size
A higher confidence level gives a higher z score. Reducing z and increasing number of samples could reduce the margin of error.
To reduce the margin of error, the correct options are
A) They could construct the confidence interval with a lower confidence level than they previously used.
B) They could include a greater number of subjects in the experiment.
For the study described below, identify the population parameter. A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. 27 of the 300 people were extremely dissatisfied with the amount of time they had had to wait in line in recent months.A) The 300 customers poll
B) The 27 people who were dissatisfied
C) The customers who were waiting in line at the bank the day of the poll
D) All customers of the bank
Answer:
The population parameter is the average wait time for all the bank's customers.
Step-by-step explanation:
The population parameter is a numerical value that defines a specific characteristic of the population. For example, the population mean describes the average value of the population, the population variance describes the variance of the population and the population proportion describes the proportion of a certain variable in the population.
The sample statistic is a numerical value that defines a specific characteristic of the sample that is selected from the population. The examples of sample statistic are, sample mean, sample variance and sample proportion.
In this case it is provided that the bank manager wants to know the average amount of time customers of his bank have to wait in line.
The experiment involved, asking 300 customers about their average wait time at the bank.
So, the parameter under study is the mean time the customers have to wait at the bank.
Hence, the population parameter is the average wait time for all the bank's customers.
Final answer:
The population parameter the bank manager wants to know is the average wait time for all customers of the bank, which is represented by option D) All customers of the bank.
Explanation:
The population parameter the bank manager is interested in determining is the average wait time for all customers of the bank, not just the 300 polled customers or the subset of dissatisfied customers. Therefore, the correct answer to the student's question is D) All customers of the bank.
This average wait time is a parameter that describes some aspect of the entire population of the bank's customers. In terms of statistics, a population parameter is a value that represents a characteristic of the entire population, which in this case, includes all the customers of the bank, whether they were part of the survey or not.
En la primera fase del proceso selectivo para Al cuerpo de profesores eliminan a cuatro novenos De los aspirantes mientras que en la segunda fase eliminan A 5/7 de los que superaron la primera fase Si se presentaron 315 aspirantes cuál es la fracción De los aspirantes que han superado las dos fases Del proceso selectivo?
Answer:
The fraction of the applicants who have passed the two phases of the selection process is [tex]\frac{10}{63}[/tex].
Step-by-step explanation:
The question is:
In the first phase of the selection process for the body of teachers they eliminate four-ninth of the applicants while in the second phase they eliminate 5/7 of those who passed the first phase. If there were 315 applicants what is the fraction of the applicants who have passed the two phases of the selection process?
The total number of applicants is
N = 315.
It is provided that 4/9th of the applicants were eliminated in the first phase.
Then the fraction of candidates who passed the first phase is:
Fraction who passed phase I = [tex]1-\frac{4}{9}=\frac{5}{9}[/tex]
Now, it is also provided that 5/7 of those who passed the first phase were eliminated in the second phase.
Then the fraction of candidates who passed the second phase is:
Fraction who passed phase II = [tex]1-\frac{5}{7}=\frac{2}{7}[/tex]
That is, 2/7 of the remaining applicants passed the second phase.
The fraction of the applicants who have passed the two phases is:
[tex]\frac{5}{9}\times \frac{2}{7}=\frac{10}{63}[/tex]
Thus, the fraction of the applicants who have passed the two phases of the selection process is [tex]\frac{10}{63}[/tex].
A tiny but horrible alien is standing at the top of the Eiffel Tower (which is 324324324 meters tall) and threatening to destroy the city of Paris! A Men In Black agent is standing at ground level, 545454 meters across the Eiffel square, aiming his laser gun at the alien. At what angle, in degrees, should the agent shoot his laser gun? Round your final answer to the nearest tenth. ^\circ ∘ degrees
Answer:
A tiny but horrible alien is standing at the top of the Eiffel Tower (which is 324 meters tall) and threatening to destroy the city of Paris! A Men In Black agent is standing at ground level, 54 meters across the Eiffel square, aiming his laser gun at the alien. At what angle, in degrees, should the agent shoot his laser gun? Round your final answer to the nearest tenth
The agent shoot his laser gun at 80.5 degree.
Step-by-step explanation:
Given:
Height at which the horrible alien is standing = 324 m
Distance from the (tower) where the agent is = 54 m
According to the question:
Men In Black agent is aiming his laser gun to shoot the horrible alien.
Let the angle at which the agent shoot his gun be " Ф "
As from the situated depicted we can draw a right angled triangle.
Using trigonometric ratios:
tan (Ф) = opposite/ adjacent
In triangle OPQ .
The adjacent side = 54 m
The opposite side = 324 m
⇒ Plugging the values.
⇒ [tex]tan(\phi) = \frac{opposite}{hypotenuse}[/tex]
⇒ [tex]tan(\phi) = \frac{324}{54}[/tex]
⇒ [tex](\phi) = tan^-^1(\frac{324}{54})[/tex]
⇒ [tex]\phi=80.53[/tex]
Nearest tenth it is 80.5 degrees.
So,
Men In Black must shoot the laser gun at an angle of 80.5 degrees.
Final answer:
The Men In Black agent should shoot his laser gun at an approximate angle of 30.8 degrees to hit the alien at the top of the Eiffel Tower, after correcting the typos in the question.
Explanation:
To find the angle at which the Men In Black agent should aim his laser gun to hit the alien on top of the Eiffel Tower, we must solve a right triangle problem. The height of the Eiffel Tower is given as 324 meters, not 324324324 as stated in the question, which is likely a typo, and the horizontal distance (base of the triangle) from the agent to the base of the Eiffel Tower is 545 meters, not 545454 as stated, which seems to be another typo.
We use the tan inverse function (arctan) to calculate the angle. The angle θ is found using the formula:
θ = arctan(opposite/adjacent)
If h is the height of the tower and d is the distance across the ground, the angle θ equals:
θ = arctan(h/d)
Plugging in our values:
θ = arctan(324/545) ≈ arctan(0.5945)
Now we find the arctan of 0.5945 using a calculator:
θ ≈ 30.8 degrees
Therefore, the agent should shoot his laser gun at an angle of approximately 30.8 degrees.
Home CoworkHelper
A
A cylinder has a volume of 10 m' What might its dimensions be (height, area of base, radius, and
diameter)? Give 4 possible cylinders.
Volume 10 m
Height
Area of Base
Radius
Diameter
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
How many possibilities are there? Why do you think so?
B. A cylinder has a diameter of 10 cm. What might its volume be? Give the radius, area of base and
height for 4 possible volumes
Diameter 10 cm
Radius
Area of Base
Height
Volume
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
Answer:
See below.
Step-by-step explanation:
PROBLEM A
The formula for the volume of a cylinder is
V = πr²h, where πr² is the area of the base.
V = area of base x height
Choose any four numbers that are less than 10 for the height.Then, substitute into the formula and isolate "r". 10 = πr²hDouble "r" to find the diameter.The area of the base is found (bolded) while you solve πr².*I will use the calculator button for pi (π)
Cylinder A: h = 1
10 = πr²h
10 = πr²(1)
10 = πr² Area of the base is 10m².
r = √ (10/π)
r = 1.78 Radius is 1.78m.
d = 2r = 1.78*2 = 3.56 Diameter is 3.56m.
Cylinder B: h = 2
10 = πr²h
10 = πr²(2)
5 = πr² Area of the base is 5m².
r = √ (5/π)
r = 1.26 Radius is 1.26m.
d = 2r = 1.26*2 = 2.52 Diameter is 2.52m.
Cylinder C: h = 4
10 = πr²h
10 = πr²(4)
2.5 = πr² Area of the base is 2.5m².
r = √ (2.5/π)
r = 0.89 Radius is 0.89m.
d = 2r = 0.89*2 = 1.78 Diameter is 1.78m.
Cylinder D: h = 5
10 = πr²h
10 = πr²(5)
2 = πr² Area of the base is 2m².
r = √ (2/π)
r = 0.80 Radius is 0.8m.
d = 2r = 0.80*2 = 1.6 Diameter is 1.6m.
The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.
There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.
PROBLEM B
Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.
We need the radius, which is half the diameter. r = d/2 = 10/2 = 5
Choose a random number for volume that divides easily by 25.Substitute "V" and "r²" (r² = 25).Isolate "h".The area of the base is 78.54 cm² every time (A = πr²).Cylinder A: V = 100
100 = π25h
4 = πh
h = 1.27 The height is 1.27m.
Cylinder B: V = 200
200 = π25h
8 = πh
h = 2.55 The height is 2.55m.
Cylinder C: V = 75
75 = π25h
3 = πh
h = 0.95 The height is 0.95m.
Cylinder D: V = 125
125 = π25h
5 = πh
h = 1.59 The height is 1.59m.
The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.
A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles:
Answer:
5/33
Step-by-step explanation:
5/12 * 4/11 = 20 /132 = 10 / 66 = 5 / 33
The probability of drawing a red marble on the first try is 5/12 because there are 5 red marbles and 12 marbles in total. The second time you only have 4 red marbles left and 11 marbles left in total. Multiply them to find the probability of drawing 2 red marbles in a row.
Probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Here,
Number of red marbles = 5 marble
Number of green marbles = 7 marble
Probability = Number of favorable outcome / Number of total outcome
Probability of drawing 1 red marble = [tex]\frac{5}{12}[/tex]
Probability of drawing second marble is red = [tex]\frac{4}{11}[/tex]
Probability of drawing 2 red marbles = [tex](\frac{5}{12})(\frac{4}{11} )=\frac{5}{33}[/tex]
Hence, the probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]
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What is the seventh term of the geometric sequence with a first term of 729 and a common ratio of ?
Given:
Given that the first term of the geometric sequence is 729.
The common ratio is [tex]\frac{1}{3}[/tex]
We need to determine the seventh term of the sequence.
Seventh term:
The seventh term of the sequence can be determined using the formula,
[tex]a_n=a_1(r)^{n-1}[/tex]
To find the seventh term, let us substitute n = 7 in the above formula, we get;
[tex]a_7=a_1(r)^{6}[/tex]
Now, substituting [tex]a_1= 729[/tex] and [tex]r=\frac{1}{3}[/tex], we get;
[tex]a_7=729(\frac{1}{3})^{6}[/tex]
[tex]a_7=729(\frac{1}{729})[/tex]
[tex]a_7=1[/tex]
Thus, the seventh term of the geometric sequence is 1.
Bruce is going to call one person from his contacts at random. He has 35 total contacts. 15 of those contacts are from his neighborhood. What is the probability he calls a person not from his neighborhood? Write your answer as a simplified fraction .
Answer:
do 35 divided by 15 then just put that into fraction form
Step-by-step explanation:
Answer:
two fifths is the answer because you would divide 15 by 35 to get .4 which is two fifths.
Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. What is the direct distance to her aunt's house?
Answer:
39 miles
Step-by-step explanation:
The given distances are at right angles to each other, so form the legs of a right triangle whose hypotenuse is the straight-line distance of interest. The Pythagorean theorem can be used to find the length of the hypotenuse.
__
Your familiarity with Pythagorean triples lets you recognize the ratio of the distances, 15/36 = 5/12, means the triangle of interest is a multiple of the (5, 12, 13) Pythagorean triple. The multiplier is 3, so ...
the direct distance to her aunt's house is 39 miles.
__
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides:
c² = a² +b²
c = √(15² +36²) = √1521 = 39 . . . . hypotenuse for legs 15 and 36
__
Some Pythagorean triples you will run across in algebra, geometry, and trig problems are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)
As here, you will also see multiples of these.
Suppose AC = 5 cm, BC = 12 cm, and mAC = 45.2°.
To the nearest tenth of a unit, the radius of the circumscribed circle
is __?__ cm and m∠OAC = __?__°.
Help pls
9514 1404 393
Answer:
6.5 cm67.4°Step-by-step explanation:
AB is shown as a diameter, which means that inscribed angle C is a right angle. The length of the diameter can be found from the Pythagorean theorem to be ...
AB^2 = AC^2 + BC^2
AB = √(5^2 +12^2) = 13
The radius is half the length of the diameter, so is ...
OA = 13 cm/2 = 6.5 cm . . . . radius
__
The measure of inscribed angle B is half the measure of arc AC, so is ...
∠B = 45.2°/2 = 22.6°
The measure of angle OAC is the complement of this, so is ...
∠OAC = 90° -22.6°
∠OAC = 67.4°
Answer:
Step-by-step explanation:
3(2x - 1) =
1
2
(4x - 2) + 2
Answer:
x=1
Step-by-step explanation:
HOPE I HELPEDPLZZ MARK AS BRAINLIEST !!!What is the area of the figure?
10.2 in.
3 in.
3 in
2 in.
2 in.
8 in.
6.2 in
Answer:
B. 80.2
Step-by-step explanation:
The easiest way to find the area of this figure is to divide it into two rectangles.
First, let's find the area of the top rectangle.
10.2 * 3 = 30.6
The area of the top rectangle is 30.6 square in.
Now let's find the area of the second rectangle:
6.2 * 8 = 49.6
The area of the bottom rectangle is 49.6 square in.
Lastly, we have to add the areas of the two rectangles together.
30.6 + 49.6 = 80.2
The area of the entire figure is 80.2 square inches.
A plane flies from NY to Chicago, which is about 700 miles, at a speed of 330 mph. How long does the flight take? On a return trip, a tailwind (x) helps the plane move faster. (The plane still operates to produce a basic speed of 330 mph. The total flying time for the round trip is 3.7 hours so how fast is the tailwind?
The flight from NY to Chicago took roughly 2.12 hours, while the return flight took about 1.58 hours due to a tailwind. By using these times to calculate the speeds of the flights, we find that the tailwind was 113.04 mph.
Explanation:The flight time from NY to Chicago can be calculated by dividing the distance (700 miles) by the speed of the plane (330 mph). The result is about 2.12 hours. The total flight time for the round trip is given as 3.7 hours, so the return trip took about 1.58 hours. Divide 700 miles by 1.58 hours and we get a total speed of about 443.04 mph for the return trip. This speed includes both the speed of the plane (330 mph) and the speed of the tailwind (x). Therefore, to find the speed of the tailwind, subtract the speed of the plane from the total speed: 443.04 mph - 330 mph = 113.04 mph. So, the tailwind is 113.04 mph.
Learn more about tailwind here:https://brainly.com/question/17522255
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The tailwind speed is found to be approximately 113.04 mph.
Let's find out the time it takes for the initial flight from NY to Chicago.
Distance from NY to Chicago: 700 milesSpeed of the plane: 330 mphTime = Distance / Speed = 700 miles / 330 mph ≈ 2.12 hoursNow, for the return trip, let the tailwind speed be denoted as x.
Speed of the plane with tailwind = 330 + x mphTotal flying time for the round trip: 3.7 hoursLet time for the return trip be t hours. Then, we have:
Time for round trip: 2.12 hours (to Chicago) + t hours (returning)So, t = 3.7 - 2.12 = 1.58 hoursTherefore, the equation for the return trip will be:
700 miles / (330 + x) = 1.58 hoursSolving for x:
330 + x = 700 miles / 1.58 hours ≈ 443.04 mphx ≈ 443.04 - 330 = 113.04 mph
The speed of the tailwind is approximately 113.04 mph.
Which of the following is a correct equation for the linear graph shown below?
(1) 2y+3x=-6
(2) 3y-2x=-6
(3) 2y+3x-2
(4) 3y-2x=-2
Given:
Given that the graph of the line.
We need to determine the equation of the line.
Slope:
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute any two points that the line passes through.
Substituting the point (3,0) and (0,-2) in the formula, we get;
[tex]m=\frac{-2-0}{0-3}[/tex]
[tex]m=\frac{-2}{-3}[/tex]
[tex]m=\frac{2}{3}[/tex]
Thus, the slope of the equation is [tex]m=\frac{2}{3}[/tex]
y - intercept:
The y - intercept of the equation is the point at which the line passes through the y - axis.
Thus, from the graph, the value of y - intercept is b = -2.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y = mx+b[/tex]
Substituting the values, we have;
[tex]y=\frac{2}{3}x-2[/tex]
Taking LCM, we have;
[tex]y=\frac{2x-6}{3}[/tex]
Multiplying both sides by 3, we get;
[tex]3y=2x-6[/tex]
Subtracting both sides by 2x, we get;
[tex]3y-2x=-6[/tex]
Thus, the equation of the line is [tex]3y-2x=-6[/tex]
Hence, Option 2 is the correct answer.
cuanto es 7x8-(31-61)
Answer:
la respuesta es 86
Step-by-step explanation: